1. Field of the Invention
The present invention concerns a method for determining an abort criterion during acquisition of two-dimensional images of a three-dimensional subject. The present invention also concerns a computer program product and an apparatus operating according to the method.
2. Description of the Prior Art
Methods of the above type are particularly necessary in x-ray imaging.
In each x-ray recording, the acquired two-dimensional (x-ray) detector signal (=the image) is used, among other things, to ascertain by means of the subject itself (in particular its absorption characteristics), the detector position relative to the subject and the source position relative to the subject. As used herein, the term “position” also can include the orientation of the x-ray detector or the x-ray source, if need be. Image I can therefore be written as:I=P O.wherein I is a vector that contains the entirety of a two-dimensional image, O is a vector that contains the volume elements of a three-dimensional subject, and P is an image matrix. In particular, they are ascertained relative to the subject by the positions of the x-ray source and the x-ray detector.
For a single projection, meaning a single image, the equation system above is generally not resolvable, i.e., the image matrix P is not invertible. The inversion is in fact ambiguous or undetermined. Given only one recording or only a few recordings, normally only a two-dimensional rendering of the projection of the subject is possible, but not a three-dimensional reconstruction of the subject.
With every further projection, further information is acquired about the subject. According to the Feldkamp algorithm, it is possible to calculate a three-dimensional reconstruction of the subject if x-ray source and x-ray detector rotate at least 180° around the subject on a common orbit. Along with the reconstruction of the three-dimensional subject per se, any two-dimensional projections as well as cross-sections are calculable and viewable. The Feldkamp algorithm is, for example, specified in “Image Reconstruction from Projections: The Fundamentals of Computerized Tomography”, G. T. Herman, Academic Press, New York, 1980.
Rotation of the source and detector through at least 180° in a common orbit around the subject ensues in the fields of computed tomography and 3D-angiography. For example, in the field of computed tomography, it is further known in U.S. Pat. No. 6,028,907 and U.S. Pat. No. 5,612,985 to linearly move the subject perpendicular to the plane of the rotation simultaneously together with the rotation of the x-ray source and x-ray detector, such that, in effect, the x-ray source and the x-ray detector describe a helical path around the subject. In this case, a three-dimensional reconstruction is possible when the linear movement of the subject is not too large. A conversion into a circular motion around the subject must be possible—for example by interpolation.
As implemented above, the solution according to Feldkamp is to presume a predominantly circular motion of the x-ray source and the x-ray detector on a common orbit. The x-ray source and the x-ray detector thereby face one another with respect to the center of rotation. If the x-ray source and/or the x-ray detector effect something other than a circular motion around the axis of rotation, the reconstruction algorithm of Feldkamp is not applicable. A technique known as the ART-Method (ART=Algebraic Reconstruction Technique) is known from G. T. Herman, A. Kuba, Discrete Tomography: Foundations, Algorithms, and Applications, Springer Verlag, Telos, 1999. By means of this method, a reconstruction of a three-dimensional subject is possible in principle from a number of projections that can lie randomly. In particular, it is thus not essential in the acquisition of the images for the x-ray source and the x-ray detector to be rotated or otherwise moved on a common orbit around the subject.